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Re: When to use "to" and "for"

then 'buy a car' flows from 'determine' Also 'buy a car' is a nounal phrase (not even a verb anymore dude)

TO talks about the actions coming from the determination

In your sentence, "the fat burning zone" is something that is determined based on the person, so 'determined fat burning zone' flows from 'that person' The flow is the reverse of the first sentence above.

FOR talks about the conditions that led to the determination

Lastly I would put another 'for in your sentence as well.

"For the cardio exercise to be effective in burning fat (effectively burn fat), the fat burning zone should be determined for each individual person."

Hope that helps. This stuff is really hard even for teachers to explain, and any rule I give may well break down. Try practicing with some simple ones:

I bought a present ______ my wife.
I brought a present ______ my wife.
I stopped ______ coffee.
I stopped ______ drink coffee.
Here, I am giving it ____ you.
Here, I was saving it ____ you.
What did you say that ____!?
Who did you say that ____!?

Re: When to use "to" and "for"

If you look at these examples, you will see that most of the uses of 'to' are different- infinitives or the preposition goes with something else in the sentce, like 'to which it belongs' and 'to a large extent'.

determine for:
1 A1B as there is not (a more piercing uncertainty) anything to determine for us whether "the broadbacked figure drest in blue and green
2 EBA the grassroots levels; particularly the right of the people to determine for themselves what developmental processes best fulfils their aspirations; f a
3 FDC them, but in the final analysis should be free to determine for itself what the child's best interests require. (4
4 FEX . The careful design of the diet will allow you to determine for yourself which foods you can tolerate and which you can not
5 FP2 It has been contended accordingly that managers should be allowed to determine for themselves how thoroughly they need investigate the background to a transaction
6 HH3 life is when she can pick and choose her customers and determine for herself the relationship she will have with them. Then a
7 J6R , because if his power is restricted to a power to determine for certain specified purposes, he may lose the power altogether if
8 JSH that they would not increase prescription charges. Ministers of course always determine for themselves whether they answer by means of a written question or whether they
9 JXJ law, about the soundest conception of justice --; that will determine for him which elaboration of abstract convention

determine to:
1 AMM . To identify any animal properly, the first stage is to determine to which phylum it belongs. Of course even the phyla themselves originated
2 B2C , and the immediate post-mortem circumstances of their remains, will determine to a large extent whether they are left in exposed or protected
3 C8R Lords would have to accept that, but would almost certainly determine to exact a price at the next opportunity. Much of this
4 CE1 markedly in old age, and whilst it is difficult to determine to what extent this is caused by, or is the cause
5 FAC be termed the technical conception of a hierarchical level. To determine to which technical level an element belongs, one needs only to
6 FBV 94; 63 L.T. 805, that is to say the court sought to determine to what extent the law, having regard to the nature of
7 FCG to define with greater precision points at which they may tentatively determine to depart from the agreed package. That should concentrate their mind
8 FCJ grant of nationality, and the member states are free to determine to whom they will grant or refuse their nationality, in the
9 G0X superstitiously, reflecting that if anyone called her Stan she would determine to get her own back on him. "Beuno,"
10 HAJ career. The nature and quality of your basic training will determine to some considerable degree your future prospects. Many authorities offer high
11 HBS you of your duties then the Board may in its discretion determine to pay you compensation in respect of that termination